Combine the sugar, 1 cup water, ginger
and grapefruit zest in a small saucepan
; bring to a boil over high heat, stirring until the sugar
dissolves. Remove from the heat and add most of the mint leaves. Let cool to room temperature, then chill for at least 4 hours and up to 24 hours.
the simple syrup
into a small bowl and discard the solids. Divide the grapefruit segments, lime
pieces and the remaining mint leaves between two tall glasses. Add a few tablespoons of simple syrup to each and muddle
. Fill the glasses with ice cubes; stir 2 tablespoons of the rum into each and fill with sparkling wine
. Stir, garnish
sprigs and serve.